MHF4U - Advanced Functions (University Preparation)
This course extends students' experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
Prerequisites:
Mark Breakdown:
Unit Tests: 70%
Final Exam: 30%
This page will have a daily breakdown of the course. Most recent classes are at the top of the page, while the older classes get pushed to the bottom.
The beginning of each unit will be marked in blue.
Evaluations (e.g., tests, assignments, quizzes) will be marked in red.
University of Waterloo CEMC Courseware for MHF4U & MCV4U
Corrections to MHF4U Textbook Answer Section
Full Course (all video lessons, completed notes, assigned homework, extra resources)
| Date | Topic / Lesson |
Extra Resources |
Assigned Work |
| J25 |
Final Exam Friday, January 25th Room 205 9am (textbook return 8:45am) |
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|
J24 J23 J22 J21 J18 J17 |
Exam Review |
p.188 #1,2,4,6,8-11,14,15,20,22,23,24,26-30 p.380 #1,2,4,5,6,8-25,27 p.580 #1-6,8,9,11,12,14,16,18,19,21,22,26,29,31,32,34 |
|
| J16 | Test - Combinations of Functions | ||
| J15 |
Review - Combinations of Functions | p.576 # 2, 4, 5, 6bcd, 7cd, 8, 9, 11, 12d | |
| J14 |
Solving Equations & Inequalities |
p.560 # 1, 3, 4, 5ef, 6ace, 9bdf | |
| J11 | work period | ||
| J10 | work period | ||
|
J09 |
Composition of Functions |
p.552 # 1, 2abf, 3, 5aef, 6def, 7cf, 10, 13 | |
| J08 |
Dividing Functions |
p.542 # 1, 2, 3 p.544 # 3, 4, 6 |
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| J07 |
Multiplying Functions |
p.537 # 1ae, 3, 4bef, 5bef, 8ad, 11, 12 | |
| D20 |
Adding & Subtracting Functions |
p.528 # 1ace, 2, 3, 5, 7, 9acef, 10, 11, 13 | |
| D19 | Exploring Combinations of Functions | p.520 # 1, 2 | |
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Unit 7: Combinations of Functions |
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| D18 |
Test - Logarithmic Functions | ||
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D17
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Review |
*** look at all notes & homework *** p.510 # 1, 2, 3, 6a, 7, 8, 10, 11bc, 13, 14ac, 15bd, 17, 19, 22, 23 |
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| D14 |
Rates of Change in Log Functions |
p.507 # 4, 7acd, 11abc Note: 7b equation y=0.0017(1.7698)^x |
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| D13 | work period | ||
| D12 |
Solving Exp & Log Problems |
Worksheet - Word Problems |
p.499 # 1, 2, 3, 5a, 6a, 11, 13, 15 |
| D11 |
Work Period |
p.485 # 4, 6bc, 7, 11 p.492 # 3, 9 |
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| D10 |
Solving Exp & Log Equations |
p.485 # 2, 8, 10, 17 p.491 # 4, 5, 7, 12 |
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| D07 |
Laws of Logarithms |
p.475 # 5, 6, 7, 9ace, 10ace, 11bde, 17 |
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| D05 |
Evaluating Logarithms |
VT - Changing Base of Logs |
p.466 # 3 (using rule 1 or 2), # 5 (using 1 or 2), 8 (using 4), 6, 9, 12, 17 |
| D04 |
Graphs & Transformations of Log Functions |
Worksheet - Transformations |
p.456 # 1-3 (basics), 4, 5, 8, 9, 11 |
| N28 |
Introduction to Logarithmic Functions |
Handout - Graphs of Exp & Log Functions |
p.451 # 4 - 9 |
| Unit 6: Exponential & Logarithmic Functions | |||
| D03 |
Test: Trig Identities & Equations | ||
|
N30 N29 |
Review | p.440 # 1, 2, 3ac, 4, 5, 6, 7, 8, 9, 10, 11b, 12bcd, 13 | |
| N27 | work period | ||
| N26 |
Solving Quadratic Trig Equations class notes |
p.436 # 1, 3, 6ac, 7bd, 8ad, 9ac, 11, 14, 18
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|
| N23 | PD Day | ||
| N22 | assembly | ||
| N21 |
Solving Linear Trig Equations |
Quiz Solutions - Compound & Double Angles |
p.426 # 1bdf, 2bdf, 5, 6bdf, 8, 10bef, 11, 18 |
| N20 | work period | ||
|
N19 |
Trigonometric Identities |
MCR3U: WS 3.3 Trig Identities(solutions) MHF4U: WS Trig Identities (solutions) |
p.416 # 5, 8, (9, 10, 11)(odd), 17 |
| N16 |
Double Angle Formulas |
p.407 # 1-3, 5, 6, 8, 9 (see p.406), 13 | |
| N15 |
Compound Angle Formulas (Addition & Subtraction Identities) |
Worksheet - RAA & CAST Rule (w/ Answers) |
p.400 # 1-4, 5acf, 6cde, 8, 9ade, 10, 13 |
| N14 |
Equivalent Trigonometric Functions |
Trig Identities Sheet |
p.392 # 1, 2a, 3acd, 4a, 5abc |
| Unit 5: Trigonometric Identities & Equations | |||
| N13 | Test: Trigonometric Functions | ||
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N12 N09 |
Review: Trigonometric Functions | p.376 # 1-4, 6, 7, 10, 11bd, 12, 14-17, 19 | |
| N08 | Activity: Model Periodic Data | ||
| N07 |
Rates of Change in Trigonometric Functions no video lesson |
p.369 # 1 - 3, 4bd, 6, 7, 8, 12, 15 | |
|
N06 N05 |
Modelling with Trigonometric Function |
Solutions: 1 2 3 4 5 6 7 8 9 10 |
p.360 # 1-3, 5, 6, 7, 9, 11 |
| N02 |
Graphs of Reciprocal Trig Functions |
worksheet | p.353 # 1, 2, 3, 6, 7 |
| N01 |
Transformations of Trig Functions |
p.343 # 1bd, 3, 4, 5, 8ade, 9, 11, 12, 14 | |
| O31 |
Graphs of Trig Functions (focus on tangent function) |
Video: Sine Graph from Circular Motion |
p.336 # 2c, 3, 5 |
| O30 |
Radian Angles in the Cartesian Plane |
Worksheet - RAA & CAST Rule (w/ Answers) MCR3U Trig Lessons |
p.330 # 1-4, 5ace, 6ace, 7ace, 8ace, 9, 11, 13 |
| O29 |
Radian Measure |
p.320 # 1 - 4, 6 - 10, 15 | |
| |
MCR3U Materials/Skills |
Trigonometry of Any Angle - CAST Rule VT (SS) - Exercises w/ CAST & Trig Ratios (TOO LOUD!) VT (SS) - Solving Linear Trig Equation using RAA & CAST Rule |
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| Unit 4: Trigonometric Functions |
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| O26 | Test: Polynomial & Rational Inequalities | ||
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O25 O24 |
Review - Polynomial & Rational Functions |
p.240 # 1ac, 2, 3, 4, 6ad, 7ad, 8bd, 10a, 11, 14c, 15, 16 p.308 # 1, 2, 3bd, 5bd, 7bc, 8, 9, 10cd, 11, 12, 13 |
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| O23 |
Rates of Change in Rational Functions no video lesson |
p.303 # 1, 2, 4, 6bc, 10, 13 | |
| O22 |
Solving Rational Inequalities |
p.295 # 1, 4acf, 5ace, 7, 9, 13 | |
| O19 |
Solving Rational Equations |
p.286 # 5ace, 6bcf, 10, 12, 13 (see p.278 for help on 10, 13) |
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| O18 |
Graphing Rational Functions |
Sample Problem PDF VT |
p.272 # 1, 3, 5bcd, 6bd, 14 |
| O17 |
Rational Functions & Asymptotes |
p.262 # 1, 2, 3 | |
| O16 |
Graphs of Reciprocal Functions |
p.254 # 1, 2def, 6bcd, 8bdf, 9bc, 11, # 16 (find equation of reciprocal (shown) and original function) |
|
| O15 |
Rates of Change in Polynomials |
p.235 # 5cde, 6cde, 7, 9, 11 | |
| O12 |
Solving Nonlinear Inequalities Algebraically |
p.225 # [1bd, 2, 3] fundamentals 5, 6bdf, 7bdf (no graph or use tech), 8, 10, 11, 15 18 [not taking up] |
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| O11 |
Solving Linear Inequalities |
p.213 # 5bdf, 6be, 7bdf, 8, 9, 11, 15, 19 |
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| O04 |
Solving Polynomial Equations |
p.204 # 6, 7ad, 10, 13, 16 | |
| Unit 3: Equations & Inequalities | |||
| O10 | Test: Polynomials | ||
| O09 |
Review - Polynomials |
p.161 # 3 - 9 p.184 # 1-3, 7, 9bdf, 10bd, 11ac, 12b, 14ad, 15bd, 16ac, 17bd |
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| O03 |
Factoring Cubic Polynomials video lesson |
WS - Factoring Sum & Difference of Polynomials (H/W on WS) |
|
|
O02 O01 |
Factoring Polynomials |
KA - Example - Remainder Theorem |
p.176 # [1-3][basics], 4bf, 5ac, 6abc, 7df, 8, 9, 10, 13, 17 |
| S28 |
Dividing Polynomials |
p.168 # 1, 4, 5ace, 6ace, 7ac, 8d, 9ac, 10ace, 11, 12, 14 | |
| S27 |
Transformations of Polynomials |
p.155 # 2, 3, 4bde, 5, 6bde, 7, 8, 9ace, 10, 11, 14 | |
| S26 |
Characteristics of Factored Form |
p.146 # 1, 2, 4, 6, 9, 10, 12, 13, 14 | |
| S25 |
Characteristics of Polynomials |
p.136 # 5, 7, 8, 9, 12, 14, 15, 16 | |
| S21 |
Polynomial Functions |
[VT - Pascal's Triangle & Binomial Expansion] |
p.127 # 1 - 5 |
| Unit 2: Polynomial Functions | |||
| S20 | Test: Functions & Rate of Change | ||
| S19 |
Review - Functions & Rates of Change |
p.60 # 1-4, 6, 7-9, 10-17 p.116 # 2-7 note: many better questions in daily homework |
|
| S18 |
Graphical Representations of Rate of Change |
p.103 # 3, 5, 9, 10 p.111 # 2, 10, 13 |
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| S17 | work period | ||
| S14 |
Average & Instantaneous Rates of Change |
p.76 # 8, 9 p.85 # 4, 7, 9, 10, 15 |
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S13 |
Combinations of Functions (using simple arithmetic operations) |
Try to complete Ex.2 & Ex.3 on your own p.57 # 2, 3, 4, 5, 6 |
|
| S12 |
Piecewise Functions |
KA - Piecewise Example | p.51 # 3, 4, 5cd, 6, 8, 9, 11, 13 |
| S11 |
Function Inverses |
KA - Restricting Domain for Inverse Functions |
p.44 # 4, 5, 6bd, 7, 9, 11, 12c, 13, 17 |
| S10 |
Review: Transformations of Functions |
handout |
p.36 # 4, 5, 6, 7, 9, 10, 15, 16ab |
| S07 |
Properties of Graphs |
p.23 # 12, 3, 4, 5, 7, 8, 9, 10, 14 use handout for 12, 14 |
|
| S06 |
Absolute Value Function |
p.16 # 3-10 | |
| S05 |
Review - Functions, Domain, Range |
Khan Academy - What is a Function? (there are several videos in series) |
p.11 # 1, 2, 3, 4, 6, 8, 11, 12, 14 |
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Unit 1: Functions & Rates of Change |
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| S04 |
Course Intro |
"Getting Started" from Ch.1, 2, 3 (hand in tomorrow) |
Full Course (all video lessons, completed notes, assigned homework, extra resources)